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geometry

Michael Assis folding a large, beige sheet or Miura-ori
statistical physics

The Atomic Theory of Origami

October 31, 2017

By reimagining the kinks and folds of origami as atoms in a lattice, researchers are uncovering strange behavior hiding in simple structures.

Classes of geometric structures
Abstractions blog

Why Mathematicians Like to Classify Things

August 15, 2017

It’s “a definitive study for all time, like writing the final book,” says one researcher who’s mapping out new classes of geometric structures.

Heavenly billiards
geometry

New Shapes Solve Infinite Pool-Table Problem

August 8, 2017

Two “rare jewels” have illuminated a mysterious multidimensional object that connects a huge variety of mathematical work.

Maryam Mirzakhani
Quantized Columns

The Beautiful Mathematical Explorations of Maryam Mirzakhani

July 24, 2017

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

Marjorie Rice
Abstractions blog

Marjorie Rice’s Secret Pentagons

July 11, 2017

A California housewife who in the 1970s discovered four new types of tessellating pentagons is dead at 94.

15 pentagon tessellations
geometry

Pentagon Tiling Proof Solves Century-Old Math Problem

July 11, 2017

A French mathematician has completed the classification of all convex pentagons, and therefore all convex polygons, that tile the plane.

Abstractions blog

How to Use a Sphere to Talk to Mars

April 12, 2017

To avoid garbled messages, mathematicians might translate them into geometric form.

Icosahedron
geometry

A New Path to Equal-Angle Lines

April 11, 2017

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

Illustration: diver searching for new math
Quantized Columns

Quantum Questions Inspire New Math

March 30, 2017

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.